The deputy Labour leader, Tom Watson, has called on the party to stop “trashing the record” of the Blair and Brown governments if it wants to win elections.

Watson used his conference speech, which won him a standing ovation, to defend the achievements of New Labour, which Jeremy Corbyn has strongly criticised over policies including the Iraq war.

“I don’t know why we’ve been focussing on what was wrong with the Blair and Brown governments for the last six years, but trashing our record is not the way to enhance our brand,” he said. “We won’t win elections like that, and we need to win elections.”

Tom Watson urges Labour to 'put band back together' in case of snap election

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Watson said it was time “to be proud of our party”, because the Conservatives were beatable and the prime minister, Theresa May, could call an election any time. “We have to believe we can win and remember how much we achieve when we do,” he said.

At one point, Watson was heckled by an audience member. He responded by pointing at her and saying: “Jeremy, I don’t think she got the unity memo.”

Observing that Labour had “ended up sounding like we were anti-business”, he said: “Capitalism is not the enemy, money is not the problem, business isn’t bad. The real world is more complicated than that, as any practical trade unionist will tell you.

“Businesses are where people work. The private sector generates money to pay for our schools and hospitals,” he said. “I don’t say this to win elections. I say it because it’s true, and people know that it’s true. That is why it wins elections.”

He congratulated Corbyn on his victory in the leadership election and made no explicit criticisms of him, but his speech homed in on the idea of showing through Labour mayors and local authorities that the party could be trusted to govern again.

Khan backed Owen Smith for the leadership and has said Corbyn was extremely unlikely to lead Labour back into No 10. In his conference speech on what is being labelled “rebels’ day”, he mentioned Corbyn only once, but ”power” 38 times.

“Labour in power. Not just talking the talk, but walking the walk too,” he said. “Never sacrificing or selling out on our ideals, but putting them in action every single day. Not a revolution overnight, but real and meaningful change that makes life easier for the people who need it most.”

He was given a standing ovation when he arrived at the main conference hall and extended applause after finishing with the words: “Conference, it’s time to put Labour back in power. It’s time for a Labour government. A Labour prime minister in Downing Street. A Labour cabinet. Labour values put into action. Conference, it’s time we put Labour back in power.”